There are many situations in which there is a need or desire to measure the rate of flow of a liquid or gas through a conduit. The federal government of the United States has set limits as to the amount of pollutants that an electric utility or other business may emit into the air. Typically, these emissions are determined from measurements of the flow rate of the stack gasses through the stack and an analysis of the stack gasses to determine the levels of pollutants which are present. Appendix A, Methods 1 and 2 of Title 40 of the United States Code of Federal Regulations, Part 60, sets forth approved methods for monitoring stack gas flow.
The measurement of flow velocity in ducts and stacks has traditionally been done using a device known as the "Type S", or "reverse-type" pitot tube. The design and calibration procedures relevant to the device have been published as ASTM Standard D-3796-90, and are essentially replicated in Method 2 of Appendix A of Title 40 of the United States Code of Federal Regulations, Part 60. FIG. 1 illustrates a typical Type S pitot tube which is well known in the art.
Essentially, the Type S pitot tube measures velocity via the differential pressure .DELTA.P between the impact pressure produced in the open end of Leg A (the tube that faces into the flow) and the venturi vacuum produced on Leg B (the tube that faces away from the flow) when the probe is aligned with the nominal flow direction. This relationship is given by: EQU V.sub.nom =(85.49 ft/sec)C.sub.p (.DELTA.p).sup.0.5 [T.sub.s /(P.sub.s M.sub.s ].sup.0.5
where:
V.sub.nom is the velocity calculated from measurements with the Type S pitot tube aligned with leg A facing into the nominal flow direction PA1 C.sub.p is the dimensionless pitot tube coefficient (nominally 0.84) PA1 .DELTA.P is the delta-pressure across the pitot tube in inches of water PA1 T.sub.s is the absolute temperature of the stack in degrees Rankin PA1 P.sub.s is the absolute static pressure of the stack in inches of mercury PA1 M.sub.s is the molecular weight of the stack gases
The calibration coefficient C.sub.p is determined via comparison with a device known as a Standard Pitot Tube, which is illustrated as FIG. 2. The standard pitot tube essentially develops its differential pressure .DELTA.P.sub.std as the difference between the impact pressure on a small hole on the upstream hemispherical boss and the stagnation pressure average across a set of small holes oriented perpendicularly to the flow. Because the Type S tube measures its impact pressure with a larger opening, and because the impact pressure is referenced to a venturi-created vacuum rather than to a stagnation pressure, the Type S tube creates a larger .DELTA.P.sub.nom than .DELTA.P.sub.std, thereby making possible the measurement of lower velocities. For this reason, and also because the larger openings in the Type S are much less susceptible to clogging, use of the Type S pitot tube has been the method of choice as a referenced method of measuring flow in dirty and/or corrosive applications.
Limitations with the prior design of the Type S pitot tube include systematic calibration bias in the presence of non-axial flow. In normal use, the Type S pitot tube is aligned with the nominal flow direction. The delta pressure associated with this orientation, .DELTA.P.sub.nom, is determined, and Equation 1 is used to calculate the gas velocity, V.sub.nom, associated with this orientation. What is desired, however, is the actual axial velocity vector, V.sub.axial, along the nominal flow direction. This is the measurement that, averaged across the stack or duct and multiplied by the cross-sectional area, will yield the actual volumetric flow.
In practice, the flow pattern is seldom axial. Non-axial flow is usually described via two parameters: "yaw angle" and "pitch angle". Both the pitch and yaw angles are measured from a line passing through the traverse point and parallel to the stack axis. The pitch angle is the angle of the gas flow component in the plane that includes the traverse line and is parallel to the nominal flow direction. By convention, the pitch angle P is defined as positive when the flow is tilted toward the probe assembly, i.e. toward the stack wall through which the probe has been inserted (See FIG. 7). The pitch angle P is defined as negative when the flow is tilted away from the probe assembly, which direction is also away from the stack wall through which the probe has been inserted. The yaw angle is defined as positive when the flow is tilted in a direction clockwise from the nominal flow direction about a line transverse to the nominal flow direction or the line of sight looking from the test port. The yaw angle is defined as negative when the flow is tilted in a direction counterclockwise from the nominal flow direction about that same line.
Since it is the goal, in using a pitot tube, to calculate: EQU V.sub.axial =V.sub.actual (Cos Y)(Cos P),
where V.sub.actual is the flow velocity along the actual direction of flow,
it follows that the ideal response of a Type S pitot tube would be: EQU V.sub.nom =V.sub.ideal =V.sub.actual [(Cos Y)(Cos P)].sup.-1
FIG. 3 shows the percent difference between V.sub.nom and V.sub.ideal over a .+-.60.degree. range of pitch and yaw angles. It is apparent that the Type S pitot tube, aligned in the nominal flow direction, will be seriously in error in the presence of nonaxial flow.
It can also be noted that the error associated with using the Type S pitot in this manner is symmetric and always positive for both positive and negative yaw angles. This penalizes users who are using the pitot tube to monitor flow for the purpose of calculating pollution emissions, but is of less concern to regulatory bodies who are more concerned that the measurement never result in an understatement of emissions. It is the policy of regulatory enforcers to eliminate negative sources of bias in emissions measurements and, indeed, the EPA is considering restricting the use of the Type S pitot tube to applications in which negative bias cannot occur.
In our paper "Fully Automated Probe Performs EPA Methods 1 and 2 for Volumetric Flow: Recent Field Experiments and Technical Enhancements", presented at the Acid Rain & Electric Utilities: Permits, Allowances. Monitoring & Meteorology Symposium on Jan. 23-25, 1995, in Tempe, Ariz., we describe a method and an automated apparatus whereby the yaw angle of the flow can be accurately measured via a Type S pitot tube which is substantially rotated into alignment with the actual yaw angle and the axial component of the flow calculated via trigonometric correction for the yaw angle. This methodology effectively eliminates errors attributable to yaw-angle flow. In circular stacks, where the yaw angle of the flow is typically more significant than is the pitch angle, this removes most of the measurement error. This method is also the subject of pending U.S. patent application Ser. No. 08/315,558 filed Sep. 30, 1994.
Examining FIG. 3 again, it is noteworthy that the error associated with pitch-angle flow is non-symmetric, being positive for positive pitch and negative for negative pitch. This is due to nonsymmetric aerodynamic interference from the support tubing. The phenomenon is of great concern to regulatory agencies who wish to eliminate all sources of negative bias. The nulling techniques which we use to handle yaw angle flow cannot be used to compensate for pitch angle where flow is being measured using a Type S pitot tube such as is shown in FIG. 1. The pitch angle flow component is at an angle toward or away from the test port. Because of the shape and construction of the Type S pitot tube it is not possible to rotate the Type S pitot tube around an axis transverse to the pitch flow direction.
It is also not practical to mathematically compensate for the pitch angle component by measuring the pitch angle using some other technique, because the type of equipment required for this is complex and not suitable for operation in many environments.
Consequently, there is a need for a more reliable and more accurate reverse type pitot tube for measuring true flow rate of a fluid through a conduit in which the effect of the pitch angle is reduced and in which negative bias is eliminated.
We have discovered that if the interference in the pitch plane is removed and if the geometry of the pitot tube in the pitch plane is symmetrical, the errors which result from the pitch angle flow are negligible in most cases and never result in a low biased reading. Our device therefore meets the goals of the regulatory agencies who desire or require that a monitoring device never give a low reading.